Question

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x−2 intersect are the solutions of the equation 4x = 2x−2. (4 points) Part B: Make tables to find the solution to 4x = 2x−2. Take the integer values of x between −3 and 3. (4 points) Part C: How can you solve the equation 4x = 2x−2 graphically? (2 points) (10 points)

Answer 1

Answer with explanation:

The equation of two curves are

y=4 x-----(1)

y=2x-2-------(2)

To find the solution of the equations above , we need to find their point of Intersection.

To find the point of Intersection of these two curves equate y values of the above two equations.

So, 4 x=2x-2 , is the required equation to find the point of intersectin of two curves.

2.

x= -3 -2 -1 0 1 2 3

LHS=4 x -12 -8 -4 0 4 8 12

RHS=2x-2 -8 -6 -4 -2 0 2 4

At, x= -1, the two , 4x and 2x-2 are equal.

3.

To solve the equation graphically

4 x=2 x-2

Plot, y=4x , and , y=4 x-2 , in the coordinate plane.The point of intersection of these two curves will give x and y value.

Answer 2

Part A:
We observe that we have the following system of equations:
y = 4x
y = 2x-2
The solution to the system of equations is an ordered pair (x, y), that is, a point in common that both functions have.

Part B:

x y = 4x y = 2x-2
-3 -12 -8
-2 -8 -6
-1 -4 -4
0 0 -2
1 4 0
2 8 2
3 12 4
The solution is the ordered pair:
(x, y) = (-1, -4)

Part C:
See attached image